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Zorluk: Çok zorDirect Proportions

A military logistics planner is calculating fuel requirements for a supply convoy consisting of 99 identical heavy transport trucks. The planned route on a tactical map measures 1010 inches, and the map's scale is 1 inch=20 miles1 \text{ inch} = 20 \text{ miles}. Field tests show that a group of 33 of these trucks operating together consumes 55 gallons of diesel fuel for every 22 miles traveled. Assuming all trucks maintain this exact rate of consumption, what is the total amount of diesel fuel, in gallons, required for the entire convoy of 99 trucks to complete the route?

  1. A
    15,000
  2. B
    240
  3. C
    75
  4. 1,500Cevap

Cevap

The total amount of diesel fuel required is 1,500 gallons.
The correct calculation involves three proportional steps: converting the map distance to actual distance (10 × 20 = 200 miles), finding the fuel rate per mile for the 3-truck group (5 / 2 = 2.5 gal/mi), and scaling this rate for the 9-truck convoy (which is 3 groups of 3). Multiplying the 3 groups by the 2.5 gal/mi rate and the 200-mile distance yields exactly 1,500 gallons.

Adım Adım Çözüm

1
Calculate the actual route distance using the map scale.
10 inches × 20 miles/inch = 200 miles.
The map distance must be converted to actual miles using the given scale to determine the true travel distance.
2
Determine the fuel consumption rate per mile for a group of 3 trucks.
5 gallons ÷ 2 miles = 2.5 gallons per mile.
Finding the unit rate (gallons per single mile) simplifies the calculation for the total distance.
3
Calculate the total fuel required for the entire convoy of 9 trucks.
(9 trucks ÷ 3 trucks/group) × 2.5 gallons/mile × 200 miles = 3 × 2.5 × 200 = 1,500 gallons.
The rate is given for 3 trucks, so we find how many groups of 3 are in the convoy (3 groups), multiply by the group rate, and then by the total distance.

Anahtar Kavram

Direct proportions in multi-step scenarios involving map scales and grouped rates.
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Direct Proportions

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